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Supporters of the legislation, which has broad bipartisan support, mobilized lobbyists — 400 from the American Cancer Society alone — and began advertising to win the votes needed to override a veto threatened by Mr. Bush. The president says the measure, which would renew and expand the State Children’s Health Insurance Program, costs too much and would be “an incremental step toward the goal of government-run health care for every American.”

The bill would cover four million children, in addition to the 6.6 million already enrolled. The overwhelming majority of those on the rolls are in low-income families. The House plans to vote on the measure as early as Tuesday, and the Senate is expected to pass the legislation a day or two later.

Federal health officials urged states to draft contingency plans in case tens of thousands of children lose coverage because of the impasse when the program expires Sept. 30. As one option, the officials said that states might consider shifting some children onto Medicaid.

Mr. Bush dispatched Michael O. Leavitt, the secretary of health and human services, to “work with states on ways to mitigate the damage that would result if Congress allows this program to lapse.”

Administration officials said they were concerned that the White House was being hurt by televised news reports that portrayed the fight as a struggle between Mr. Bush and poor children, rather than as a philosophical debate over the role of government in health care.

The Department of Health and Human Services and the Congressional Research Service estimate that a dozen states will run out of money next month if the program, known as Schip, is not extended. The two agencies said the states were Alaska, Georgia, Illinois, Iowa, Maine, Maryland, Massachusetts, Minnesota, Mississippi, New Jersey, Rhode Island and Wisconsin.

Problems in Iowa could draw national attention because presidential candidates of both parties often visit the state, and Democrats are continually talking about health care and the uninsured as a major issue in next year’s race.

Gov. Chet Culver of Iowa said: “Without a new infusion of federal dollars by the deadline, Iowa will not have sufficient federal matching dollars to pay October premiums for our children who rely on Schip for health care.”

Dr. Rhonda M. Medows, commissioner of the Georgia Department of Community Health, said that up to 273,000 children in the state would “sustain a tragic loss of health care coverage” if the federal government did not renew or temporarily extend the program.

The House and the Senate passed different versions of the legislation in early August. The compromise worked out by negotiators would renew the child health program for five years, with a total of $60 billion, which is $35 billion more than the current level of spending. The additional cost would be financed by increasing the federal excise tax on cigarettes by 61 cents, to $1 a pack.

Supporters of the compromise said they were confident they had the two-thirds majority needed to override a veto in the Senate, which passed a similar bill by a vote of 68 to 31 on Aug. 2.

It was uncertain how many House Republicans might back the compromise, though at least 16 last week signed a letter expressing support for the Senate approach.

The measure has been stripped of Medicare changes that were opposed by Republicans, but carries a price tag that makes some lawmakers nervous. “This is still awfully expensive,” said Representative Judy Biggert, Republican of Illinois, who added that she would probably vote for the legislation.

Senator Susan Collins of Maine, a Republican seeking re-election, said the president would be “making a terrible mistake” if he vetoed the bill. She urged him to reconsider his veto threat.

But the Senate Republican leader, Mitch McConnell of Kentucky, said, “I intend to support the president, to keep this bill targeted at young people it was meant to serve in the beginning.”

A liberal group supporting the legislation was scheduled to begin running a television advertisement that said Mr. McConnell had “sided with the big insurance companies” by voting against an earlier version of the legislation.

On Monday, a wide range of groups endorsed the compromise bill, saying it should be passed by Congress and signed by Mr. Bush. The groups included the American Medical Association, the American Hospital Association, America’s Health Insurance Plans and the Healthcare Leadership Council, representing insurers, hospitals, pharmacies and pharmaceutical companies.

Daniel E. Smith, vice president of the American Cancer Society, said: “The choice is simple: Are you for kids? Are you for tobacco companies? Mr. President and Congress, we hope you side with the kids.”

Mr. Bush said last week that the compromise bill would cover children in four-person families with incomes exceeding $80,000 a year, which is about four times the poverty level.

But Senator Charles E. Grassley, an Iowa Republican and co-author of the bill, said that under the compromise, a state could set its income limit at $80,000 only if the secretary of health and human services gave approval. New York is the only state that has proposed such a high limit, and the Bush administration denied its request on Sept. 7.

Representative Joe L. Barton of Texas, the senior Republican on the Energy and Commerce Committee, said that Democrats were more interested in politics than in the details of the program.

“The majority is passing a bill they know will be vetoed in hopes of making the president look as if he’s against health care for children,” Mr. Barton said.